Question: Simplify the following expression and state the condition under which the simplification is valid. $r = \dfrac{n^2 - 9}{n - 3}$
Solution: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{9} = -3$ So we can rewrite the expression as: $r = \dfrac{({n} {-3})({n} + {3})} {n - 3} $ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq 3$ Therefore $r = n + 3; n \neq 3$